Diffusion Magnetic Resonance Imaging (Diffusion MRI or dMRI) is a form of MRI that allows measurements of the diffusion of water (or other molecules) in biological tissue and has multiple applications. Diffusion weighted Magnetic Resonance Imaging (DWI) can provide a unique ability to quantify the diffusion characteristics of biological tissue. Diffusion processes can be influenced by the geometrical structure of the local environment, which can be used to probe the microstructure of biological tissue non-invasively via diffusion imaging techniques. One application of Diffusion MRI measurement is to quantify diffusion anisotropy of white matter tissue, such as for tracking neural fibers. The goal of fiber tracking is to accurately follow and quantify fibers through their entire length without interference from other fibers or other tissue and correctly getting from source to termination. Anisotropy in biological tissue can be measured by a Fractional Anisotropy (FA) map based on Diffusion Tensor Imaging and is the basis of most tractography methods. Anisotropic measurement based on FA has limitations due to its directional insensitivity and instability to the effects of crossing fibers. Other methods include variations on FA, such as Generalized Fractional Anisotropy (gFA), which can be used for advanced reconstruction methods like QBALL Imaging and Diffusion Spectrum Imaging. Some metrics like the Westin metric can classify voxels as isotropic, single fiber or crossing fiber structure. Some of these metrics are robust for describing the isotropic and anisotropic measure of a single fiber, but unreliable for a crossing fiber.
Conventional metrics such as FA have multiple drawbacks when used for fiber tracking. FA is a scalar metric which is proportional to the standard deviation of values of diffusion anisotropy in all direction at a given location. FA has two fundamental limitations. First, because it is a measure based on standard deviation, it works well for isotropic and single fiber cases, but fails in fiber crossing situations, because it combines anisotropic information from all directions. Second, FA does not provide a connectivity metric between functional regions of the human brain. It is difficult to predict axon connectivity based on the FA metric. FA is dependent on interstitial water, compression/spreading of the fiber tract, tract crossing, and local curvature. These tendencies make FA a badly confounded measure of brain connectivity.
The mismatch of a standard deviation measure such as FA and a mean measure can be seen via an analogy to measuring the strength of I-beams in a building. Engineers use finite element models that verify that each I-beam has the strength (e.g., can support a mean weight 50 tons) to support the load at that point. Using a standard deviation measure (e.g., the standard deviation of each I-Beam is 1 ton) would be a poor measure of the key variable—the load that link could support. Having beams with a 1 ton standard deviation rather than a 5 ton standard deviation does not tell you if beam will support a 50 ton weight, because standard deviation is a poor measure of the strength of a building link.
A core goal for fiber tracking is to quantify the volume of axons oriented in a specific direction within a voxel. However, FA quantifies the variance of the three principal directions, removing information regarding either the direction or count of axons in a voxel. FA is both directionless and dimensionless. While these qualities may be appealing to mathematicians, they make FA less useful for applications measurement of connective strength.
Anisotropy or connectivity is directionally dependent by nature, which scalar field quantities like FA are unable to describe. Conventional metrics are not direction sensitive, because all conventional metrics since the introduction of FA in 1990 by Moseley et al. have been scalar metrics. Another characteristics of connectivity not represented by conventional metrics such as FA that are based on the standard deviation or related quantities is the strength or magnitude of diffusion in a given voxel. Because of this, conventional metrics lack the needed reliability in fiber crossing area and strength to provide a real anatomical quantification.